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Luck is a powerful trait that gives units a 75% chance to evade any damage from external sources that would otherwise kill them.
Luck is given by:
A unit with Cursed Luck does not benefit from Luck. This effect can be caused by the Fateweaving Bless, Luck's counterpart.
Luck is amazing to have on chaff (small frontline troops who you don't count on living) and is a decent layer of protection for your weaker Commanders against ranged attacks. You shouldn't press your Luck too hard, though.